20180901, 19:35  #34 
May 2018
5·37 Posts 
In this article, they talk about rescaling gaps. There is the formula (gT)/a. I believe that this is what I want. However, the values for maximal prime gaps are not given in the article. This article talks about primes that are r mod q. Regular prime gaps are between primes that are 0 mod 1. Therefore, a(p)=p/li(p) and T(p)=(p/li(p))(2*log(li(p))log(p)). Then, the value is (g((p/li(p))(2*log(li(p))log(p))))/(p/li(p)). What are the values of this function for the known maximal prime gaps?

20180901, 20:07  #35 
"Curtis"
Feb 2005
Riverside, CA
4,211 Posts 

20180903, 03:31  #36 
Jun 2015
Vallejo, CA/.
3BC_{16} Posts 

20180903, 15:17  #37 
May 2018
5·37 Posts 
The article is about maximal gaps between primes that are r mod q. Regular maximal prime gaps are between whole numbers. Since all whole numbers are 0 mod 1, then r=0 and q=1. Therefore, regular maximal prime gaps are between primes that are 0 mod 1.

20180904, 07:07  #38 
Jun 2015
Vallejo, CA/.
2^{2}×239 Posts 
But ALL primes (except 2) are 1 Mod 2, so that is a stronger restriction. There is only 1 maximal gap that involves prime 2.

20180911, 21:37  #39 
May 2018
5·37 Posts 
The greatest gap between primes up to n is about log^{2}(n)2*log(n)*log(log(n)). Therefore, a good measure would be (g(log^{2}(p)2*log(p)*log(log(p))))/log(p)=(glog^{2}(p)+2*log(p)*log(log(p)))/log(p). Which maximal prime gap has the biggest value of (glog^{2}(p)+2*log(p)*log(log(p)))/log(p)?
Last fiddled with by Bobby Jacobs on 20180911 at 21:40 
20180912, 12:37  #40  
Aug 2006
2·3·977 Posts 
Quote:
It's not at all clear to me that we can meaningfully discuss nonleading terms when even the coefficient of the leading term is in doubt. (Some sources aren't even sure of the exponent.) 

20181011, 15:41  #41 
May 2018
10111001_{2} Posts 
Here are the values of (glog^{2}(p)+2*log(p)*log(log(p)))/log(p) for the first 30 maximal prime gaps. This measure seems to have the same distribution on all maximal prime gaps.
p_{1}: 2, 3, 7, 23, 89, 113, 523, 887, 1129, 1327, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783, 387096133, 436273009 g: 1, 2, 4, 6, 8, 14, 18, 20, 22, 34, 36, 44, 52, 72, 86, 96, 112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282 p_{2}: 3, 5, 11, 29, 97, 127, 541, 907, 1151, 1361, 9587, 15727, 19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333, 2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893, 191913031, 387096383, 436273291 (glog^{2}(p_{1})+2*log(p_{1})*log(log(p_{1})))/log(p_{1}): 0.01652201917, 0.9099618198, 1.441142842, 1.06365333, 0.2967400124, 1.340824126, 0.2842368037, 0.01113471657, 0.0008777107308, 1.483239756, 0.8055044796, 0.5695678433, 0.04079693315, 1.273888756, 0.1979231021, 0.1949205926, 1.015367394, 0.7377458039, 0.4610135033, 0.5222047529, 1.033263049, 0.1404118759, 0.2170613361, 1.258418936, 0.5201039801, 0.8502142355, 0.8892300766, 0.1730714975, 1.162682203, 0.2623211567 (glog^{2}(p_{2})+2*log(p_{2})*log(log(p_{2})))/log(p_{2}): 0.0002774068079, 0.5850019473, 1.019417059, 0.8427693921, 0.2151204219, 1.201433598, 0.2457202101, 0.03652024352, 0.02150721463, 1.44838762, 0.8100577184, 0.5731101098, 0.04431878473, 1.270502656, 0.1971322563, 0.1953011903, 1.01490609, 0.737395807, 0.4611403309, 0.5220568929, 1.033147879, 0.1403614607, 0.2170774769, 1.258402597, 0.5200965832, 0.850217021, 0.8892319752, 0.1730735353, 1.162683196, 0.2623201147 The gap with the highest value is 1327 to 1361. The gap with the lowest value is 387096133 to 387096383. Last fiddled with by Bobby Jacobs on 20181011 at 15:47 
20190227, 20:24  #42 
May 2018
185_{10} Posts 
Title vandalism
Did somebody change the title of this thread? It used to be called "A way to measure record prime gaps". Now, it is "No way to measure record prime gaps". Who vandalized the title? By the way, I have decided to call my prime gap measure (glog^{2}(p)+2*log(p)*log(log(p)))/log(p) the Jacobs value.

20190227, 21:54  #43 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
386_{16} Posts 

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